Strained coherent heteroepitaxy of III-V semiconductor films such as In$_x$Ga$_{1-x}$As/GaAs has potential for electronic and optoelectronic applications such as high density logic, quantum computing architectures, laser diodes, and other optoelectronic devices. Crystal symmetry can have a large effect on the morphology of these films and their spatial order. Often the formation of group IV strained heterostructures such as Ge deposited on Si is analyzed using analytic models based on the Asaro-Tiller-Grinfeld instability. However, the governing dynamics of III-V 3D heterostructure formation has different symmetry and is more anisotropic. The additional anisotropy appears in both the surface energy and the diffusivity. Here, the resulting anisotropic governing dynamics are studied to linear order. The resulting possible film morphologies are compared with experimentally observed In$_x$Ga$_{1-x}$As/GaAs films. Notably it is found that surface-energy anisotropy plays a role at least as important as surface diffusion anisotropy if not more so, in contrast to previous suppositions.
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